# SemanticsAssignment

## 1           An event analysis ofarguments

The grammatical roles (i.e. subject, object, etc.) of any verb can be semantically analyzed using argument roles (i.e. AGENT, PATIENT, etc.) in a logic that uses event variables.

• Bianca baked the pizza in theoven

1. Bianca baked in theoven

Answer:∃e [bake (e)∧ Agent (b, e) ∧ Location (oven, e)]

1. The pizza was baked in theoven

Answer: ∃e [ bake (e) ∧ PAT (pizza, e) ∧LOC (oven, e)]

1. Biancabaked

1. The pizza wasbaked

## 2           Quantification over tense andevents

Tense variables can be ‘re-introduced’ into a logical analysis that includes event variables. This is how it’s done.

• Camillomeowed
1. ∃t∃e [t<t0∧meow(e)∧AGENT(camillo,e)∧AT(e,t)]

Notice that last part of the formula: by using a special ‘AT ’ predicate we have a way of having the meowing event happen at the time t that is in the past, as specified higher up in the formula t < t0(alternatively tnow). That’s all there is to it!

Yourtask:Providealogicalanalysisofthefollowingsentences,includingbothtenseandeventslikein (1b)andtheotherconceptsthatwecreatepredicatesoutof(i.e.MANNER,INSTRUMENT,LOCATION, etc.)Note:therearenoindividualvariablesinanyofthesesentences.Assuch,inyourformulasyou can analyze definite descriptions like ‘the cupboard’ as in individual constant like the name ‘Camillo’ above. For example, ‘Camillo’ = camillo, and ‘the book’ = thebook.

• John will arrive late bytrain.

Note:  t= time

∃t∃e [t<t0∧ arrive (e) ∧ PAT (J, e) ∧ MANNER (late, e) ∧ INST (train, e) ∧ AT(e, t)]

• Francesca took the book fromArgo.

∃t∃e [t<t0∧ take ( e ) ∧ AGENT (Francesca, e) ∧ PAT (book, t) ∧ LOC (Argo,e) ∧ AT (e, t)]

• Wanda quickly shoved Camillo into thecupboard.

• The tree will fallsuddenly.

• Argo always mashes the carrot messily with thefork.2

2Consult your notes from Lecture 2 for an analysis of ‘always’.

## 3           Bringing it alltogether

Your task: Provide a logical analysis of the following sentences, using all the logical vocabulary you’ve learned.  These can be challenging,  and there are different ways some of these sentences can  be logically analyzed (i.e. the position of the quantifiers in the formula). Trust your skills and instincts forlogic!

• Some tree will fallsuddenly.

Note:x= some tree

∃x ∃t ∃e [t0< t ∧ tree (x) ∧ fall ( e )∧ suddenly ( e ) ∧ PAT (x, e)  ∧ AT (e, t) ]

• All of the mail will arrive late bytrain.

Note: M = mail

x [ Mx →∃e∃t [ t0< t∧ arrive ( e ) ∧ PATIENT (x, e) ∧ INST (train, e)∧ MANNER (late,e) ∧ AT (t, e) ]]

• Some cat quickly shoved a dog into abox.

• Argo made the horses run

( This is challenging but you can do it! – Think of how multiple events were ‘connected’ in lecture 2)